It is desired to enrich the partial pressure of hydrogen in a hydrogen–nitrogen gas mixture for which the partial pressures of both gases are 0.1013 MPa (1 atm). It has been proposed to accomplish this by passing both gases through a thin sheet of some metal at an elevated temperature; in as much as hydrogen diffuses through the plate at a higher rate than does nitrogen, the partial pressure of hydrogen will be higher on the exit side of the sheet. The design calls for partial pressures of 0.051 MPa (0.5 atm) and 0.01013 MPa (0.1 atm), respectively, for hydrogen and nitrogen. The concentrations of hydrogen and nitrogen (CHC H and CNC N , in mol/m3mol/m
3 ) in this metal are functions of gas partial pressures (pH2 and pN2p
H 2 and p N , in MPa) and absolute temperature and are given by the following expressions:
CH=2.5×103√pH2exp(−27,800J/mol/RT)
CN=2.75×103√pN2exp(−37,600J/mol/RT )
Furthermore, the diffusion coefficients for the diffusion of these gases in this metal are functions of the absolute temperature, as follows:
DH(m2/s)=1.4×10−7exp(−13,400J/mol/R T)
DN(m2/s)=3.0×10−7exp(−76,150J/mol/R T)
Is it possible to purify hydrogen gas in this manner? If so, specify a temperature at which the process may be carried out, and also the thickness of metal sheet that would be required. If this procedure is not possible, then state the reason(s) why.